On my main linux machine, I usually upgrade my packages pretty much without thinking about it and in the rare event that I get a compatibility issue, I solve it afterwards. I always have backups of important configuration files, but that's about it.
However, I am starting to work on a real server and I wondered how I should proceed to upgrade packages: should I look at all packages that can be upgraded and check for compatibility issues? Is there some better method?
I'm looking for any kind of advice that I can follow to be sure I can learn how to properly upgrade packages on a machine that should stay operational at all times.